It's mostly for head-games. Klutz prevents items from affecting the Pokemon with the ability, so say someone tricked a ring target onto your hypothetical Golurk to hit it with thunder wave or a fighting move (ring targets nullify type immunities when held), it wouldn't work, and Golurk would still be immune. It works the other way, too. As a Pokemon with klutz can hold a toxic orb without being poisoned before tricking it onto something else.
So yeah, klutz has dubious usefulness. For staters no positive effect items like leftovers will work. It's useless in game, as items like the toxic orb are very rare and once tricked onto another Pokemon, you don't get them back after the battle. And the AI NEVER tries to trick nasty items on you either. In game, avoid klutz like a plague rat.
In competitive, it's a different story. Pokemon there are very reliant on items, and having a safe way to take an opponent's leftovers and swap them, say, a flame orb can be all it takes to shift the battle in your favor. Other players sometimes also use trick too to do this, and having them trick it onto a klutz Pokemon essentially wastes one of their turns. Also, unless the opponent has frisk, they have no way of knowing what a klutz Pokemon's item is, making them unpredictable. That said, klutz-tricking items only works in low tiers, and only about 2 or 3 Pokemon can even do it, so... yeah.
So basically, klutz is terrible in game and useless anywhere unless you have trick or fling or something. It's good for annoying people on showdown, but not much else. It's a gimmick, really.
But at least it's better than truant, right?